Response #1: The American Veterinary Medical Association has a 6-year term limit for board members (no consecutive terms allowed) and officers generally serve one-year terms, but there are some nuances there. For example, we elect a "president-elect" who effectively has a three-year term (one year as president-elect, one year as president, one year as immediate past president). The treasurer serves a one-year term, but up to six consecutive terms. And the Executive Vice President and the Assistant EVP (both officers but staff positions) serve one-year terms with no limits on the number of consecutive terms written into the bylaws.1
Response #2: The CPA society I used to be at didn't use term limits per se but did require a hiatus before serving again. This requirement was memorialized not in the bylaws themselves, but in another document they call "Nominating Committee Protocols." The board is empowered by the bylaws to establish these protocols to help the nominating process be more consistent. (They had noticed that the various chairs of the nominating committee had their own take on the traditions of the organization governing nominations, and this gave the board a way to formalize things a bit.)
It was felt that the inner workings of the nominating committee were inappropriate to lock into the bylaws. So they went with a document that could be changed by majority vote of the board. If your organization uses Robert's Rules as its parliamentary authority, this may not fit the normal pattern set up in Robert's for a nominating committee.
Response #3: Our Bylaws specify that an elected director will serve a term of 3 years, and may serve no more than two terms (consecutive or not) in that role.
In addition to the regular director positions on the Board, one individual is elected as President-Elect each year and then serves as an officer/director for three years (President-Elect, President, Past President). The presidential role can be in addition to the two terms as an elected director. Consequently, an individual elected to the presidential role might serve as many as 9 years total on the board.3
Response #4: Our Executive Committee has considered this many times and has rejected term limits, favoring continuity, experience, philanthropic support, etc. The Board is staggered, with Trustees serving three-year terms and the committee responsible for nominations to the Board will evaluate performance and may not re-nominate at the end of three years if there is a significant lack of participation. Officers are elected each year. There is a general guideline, reflected in policies adopted by the nominating committee, that the Chair or Co-Chairs of the Board serve a three year term, but this is not in the bylaws and is not a mandatory term limit, just a guideline.4
Response #5: AAAS' bylaws have a limit of eight consecutive years (two consecutive terms), but a Board member could be elected again after a break.5